The Albion midfielder has been training twice a day with Argentina under-23s in readiness for the Olympics.
He was given clearance to compete in the Games having played a large part in helping Argentina get to Japan in the first place.
The squad have been working at their FA’s base in Ezeiza, Buenos Aires.
They have typically done strength and conditioning in morning sessions and more technical work with the ball in the afternoons.
They have a friendly against the South Korean national team next Tuesday before moving on to Japan.
Mac Allister is the only current Premier League player in the squad.
He had made it clear he hoped to be involved in both the Copa America and Olympics this summer.
But his omission from the Copa, in which Argentina have reached the final, allowed for some rest after a busy Prem season.
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